Tonally, bolt-ons tend to emphasize harmonics over fundamental frequencies, which leads many players to characterize them as "punchier" than neck throughs. From personal experience, I think that's right; they punch up the higher frequencies and generate a more ringing tone. Most of the bolt-ons I've tried beat neck throughs for slap tone.

Conversely, neck throughs emphasize the fundamental over the harmonics. The fact that there is no neck joint also helps stabilize the neck and improve low B response. To me, neck throughs generate a more organic or "acoustic" tone than bolt-ons; I think they're well-suited for fretless basses.

There's also a third method: set-neck construction, where the neck is not bolted but glued to the body (Gibson Les Paul, Le Fay Pangton). The resulting sound is (probably) somwhere in between bolt-on and neck-thru.